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Alternating Current

Question

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A device X is connected across an ac source of voltage V=V₀sin ωt. The current through X is given as $I - I_{0} \sin (ωt + \frac{π}{2})$

Identify the device X and write the expression for its reactance.

Draw graphs showing a variation of voltage and current with time over one cycle ac, for X.

How does the reactance of the device X vary with the frequency of the ac? Show this variation graphically.

Draw the phasor diagram for the device X.

Solution

Device: X-capacitor
$X_{c} = \frac{1}{2 πfC}$
$X_{c} \propto \frac{1}{f}$
phasor diagram

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